[text version]
------------------------------------
CAVEATS
------------------------------------
1) Note that if you are using the browser-based polymake like me (http://shell.polymake.org/) or (http://polymake.org/doku.php/boxdoc) you can copy from my stuff and paste into the browser by right-clicking. Be careful though because your browser/clipboard may insert line breaks, which mess it up for a big entry. Paste into notepad first and remove them.
2) I left the prompt “polytope >” in. Remove this.
3) Underscores like in F_VECTOR get removed sometimes and need replaced. Can be done in the pasting box in polymake.
4) The output below for VERTICES_IN_FACETS gives lists of the vertices, numbered 0-14, based on the order they were entered.
The pictures with the numbering 0-14 are here.
To see one of the 4d facets, you can go back and get those vertices from the original input, and make a new polytope with just those! For an example, see the facet from {0 2 3 4 7 14}
here.
5) The points here are integers via multiplying the usual ones by 8. I put the initial “1” in each point.

-----------------
Here they are again in different order, as calculated by Bill Sands:
-----------------
$points=new Matrix([[1,4,1,1,2,8,2,2,4,4,8,4,1,4,1,2],[1,4,1,2,1,8,2,4,2,4,4,8,1,4,2,1],[1,4,2,1,1,8,4,2,2,4,4,4,2,8,1,1],[1,2,1,1,4,8,4,4,4,2,8,2,1,2,1,4],[1,1,2,1,4,8,4,8,2,1,4,4,2,2,1,4],[1,1,1,2,4,8,8,4,2,1,4,2,1,4,2,4],[1,2,1,4,1,8,4,4,4,2,2,8,1,2,4,1],[1,1,2,4,1,8,4,2,8,1,4,4,2,2,4,1],[1,1,1,4,2,8,8,2,4,1,2,4,1,4,4,2],[1,2,4,1,1,8,4,4,4,2,2,2,4,8,1,1],[1,1,4,2,1,8,2,4,8,1,4,2,4,4,2,1],[1,1,4,1,2,8,2,8,4,1,2,4,4,4,1,2],[1,2,2,2,2,8,2,2,8,2,8,2,2,2,2,2],[1,2,2,2,2,8,8,2,2,2,2,2,2,8,2,2],[1,2,2,2,2,8,2,8,2,2,2,8,2,2,2,2],[1,4,2,2,4,4,1,1,2,8,8,4,1,4,1,2],[1,4,2,4,2,4,1,2,1,8,4,8,1,4,2,1],[1,4,4,2,2,4,2,1,1,8,4,4,2,8,1,1],[1,2,4,4,4,2,1,1,4,8,8,2,1,2,1,4],[1,1,4,8,2,1,2,1,4,8,4,4,2,2,1,4],[1,1,8,4,2,1,1,2,4,8,4,2,1,4,2,4],[1,2,4,4,4,2,1,4,1,8,2,8,1,2,4,1],[1,1,4,2,8,1,2,4,1,8,4,4,2,2,4,1],[1,1,8,2,4,1,1,4,2,8,2,4,1,4,4,2],[1,2,4,4,4,2,4,1,1,8,2,2,4,8,1,1],[1,1,2,4,8,1,4,2,1,8,4,2,4,4,2,1],[1,1,2,8,4,1,4,1,2,8,2,4,4,4,1,2],[1,2,2,2,8,2,2,2,2,8,8,2,2,2,2,2],[1,2,8,2,2,2,2,2,2,8,2,2,2,8,2,2],[1,2,2,8,2,2,2,2,2,8,2,8,2,2,2,2]]);